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Results for “uncertainty Quantification”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques

Here, we study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Accelerating Hamiltonian Monte Carlo for Bayesian inference in neural networks and neural operators

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network’s parameter space and the non-convexity of their posterior distributions. Therefore, various approximation techniques, such as variational inference (VI) or stochastic gradient MCMC, are often employed to infer the posterior distribution of the network parameters. Such approximations introduce inaccuracies in the inferred distributions, resulting in unreliable uncertainty estimates. In this work, we propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently and accurately quantify uncertainties in neural networks and neural operators. The proposed approach leverages an initial VI training on the full network. We examine the influence of individual parameters on the prediction uncertainty, which shows that a large proportion of the parameters do not contribute substantially to uncertainty in the network predictions. This information is then used to significantly reduce the dimension of the parameter space, and HMC is performed only for the subset of network parameters that strongly influence prediction uncertainties. This yields a framework for accelerating the full batch HMC for posterior inference in neural networks. We demonstrate the efficiency and accuracy of the proposed framework on deep neural networks and operator networks, showing that inference can be performed for large networks with tens to hundreds of thousands of parameters. Finally, we show that this method can effectively learn surrogates for complex physical systems by modeling the operator that maps from upstream conditions to wall-pressure data on a cone in hypersonic flow.

Bayesian inference↗
DOE OSTI2025

Intrepid MCMC: Metropolis-Hastings with exploration

In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive to evaluate the associated density function. For such cases, MCMC has proven to be an invaluable tool. Random-walk Metropolis Methods (also known as Metropolis-Hastings (MH)), in particular, are highly popular for their simplicity, flexibility, and ease of implementation. However, most MH algorithms suffer from significant limitations when attempting to sample from distributions with multiple modes (particularly disconnected ones). Here, in this paper, we present Intrepid MCMC - a novel MH scheme that utilizes a simple coordinate transformation to significantly improve the mode-finding ability and convergence rate to the target distribution of random-walk Markov chains while retaining most of the simplicity of the vanilla MH paradigm. Through multiple examples, we showcase the improvement in the performance of Intrepid MCMC over vanilla MH for a wide variety of target distribution shapes. We also provide an analysis of the mixing behavior of the Intrepid Markov chain, as well as the efficiency of our algorithm for increasing dimensions. A thorough discussion is presented on the practical implementation of the Intrepid MCMC algorithm. Finally, its utility is highlighted through a Bayesian parameter inference problem for a two-degree-of-freedom oscillator under free vibration.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Effects of cluster expansion on the locations of phase transition boundary as a first step to quantify uncertainty in first principles statistical mechanics framework

Predicting phase diagrams from first principle calculations eliminates the need of tedious experimental trials and errors. Fully automating first principle phase diagram calculations without any sort of human intervention has been a long daunting task and troubling scientific communities for decades. This grand problem remains not fully resolved, largely due to the vastly high-dimensional parameter space associated with density functional theory, cluster expansion, lattice Monte Carlo, and the substantial uncertainty propagating through a set of complex simulations. As a first step to tackle this grand problem, we reported a first demonstration of how sensitive phase boundary locations can be to various cluster expansion fittings and input DFT training data. To the best knowledge of the authors, this study reported the first ever attempt to quantify uncertainty in first principles statistical mechanics framework. In addition, a semi-automated phase transition detection algorithm has been devised in this paper to deal with the associated statistical errors and uncertainties from Monte Carlo method and its predecessor DFT calculations and cluster expansions. This algorithm has been applied in a classical cluster expansion Mg-Cd binary alloy system to detect phase transitions at various locations of phase diagram using different cluster expansions to demonstrate its predictive power and quantify uncertainties. The results suggested that using Chebyshev basis function shifted the transition locations toward the dilute solid solution phase and expanded the phase stability of concentrated ordered phases to wider composition range. The addition of perturbed defect configurations into training data set lowered the order-disorder transition temperature to be away from true transition temperature, suggesting the transition nature is indeed configurational disorder dominated rather than defect assisted. Finally, we found that the weighting has negligible effect on the transition locations, except for the case of using Chebyshev basis function to fit all non-weighted configurations that can be susceptible to Monte Carlo sampling hysteresis.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Bayesian calibration of strength model parameters from Taylor impact data

Materials strength plays a key role in determining the mechanical response of engineered structures. As such, accurate strength models are crucial in simulations involving complex loading conditions, particularly when deformation in the plastic regime is deemed important. In this work, a Gaussian process based surrogate for a finite element simulation of a Taylor impact test is developed and used for Bayesian calibration of the Preston–Tonks–Wallace strength model. Here, the surrogate model is shown to closely approximate the salient features of the Taylor cylinder deformation and is validated against simulation output before being used in the strength model calibration routine. The results show that Taylor impact test data can be used in the calibration of constitutive equations through the use of a combination of data science techniques, namely Gaussian processes and Bayesian inference.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Active learning for SNAP interatomic potentials via Bayesian predictive uncertainty

Bayesian inference with a simple Gaussian error model is used to efficiently compute prediction variances for energies, forces, and stresses in the linear SNAP interatomic potential. Here, the prediction variance is shown to have a strong correlation with the absolute error over approximately 24 orders of magnitude. Using this prediction variance, an active learning algorithm is constructed to iteratively train a potential by selecting the structures with the most uncertain properties from a pool of candidate structures. The relative importance of the energy, force, and stress errors in the objective function is shown to have a strong impact upon the trajectory of their respective net error metrics when running the active learning algorithm. Batched training of different batch sizes is also tested against singular structure updates, and it is found that batches can be used to significantly reduce the number of retraining steps required with only minor impact on the active learning trajectory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Data-driven surrogate modeling of hPIC ion energy-angle distributions for high-dimensional sensitivity analysis of plasma parameters' uncertainty

In this work, we present a data-driven strategy for effective construction of a surrogate model in high-dimensional parameter space for the ion energy-angle distribution (IEAD) output of hPIC simulations of plasma-surface interactions. The methodology is based on a bin-by-bin least-squares fitting of the IEAD in the parameter space. The fitting is performed in a transformed coordinate system to normalize the IEAD, and it employs sparse grids for sampling the parameter space to overcome sampling challenges in high dimensions. The surrogate model is significantly cheaper computationally than direct hPIC simulations yet maintains high fidelity to them, providing a fast emulator for hPIC simulations. Sensitivity analysis based on the surrogate model is utilized to characterize the dependence of the ion impact angle and energy moments on the physical parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costs by performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductions typically on the order of 60 or more and possibly as large as 200. Furthermore, adaptive griding results in more accurate computation of geometric quantities such as x-points associated with the model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

When physics-informed data analytics outperforms black-box machine learning: A case study in thickness control for additive manufacturing

Aerosol jet printing (AJP) has emerged as a promising noncontact additive manufacturing method for high-resolution printing for a wide range of material systems. A key challenge limiting the broader adoption of AJP in the material science community is the lack of methods to precisely control thickness. Herein, we develop a model-based design of experiment (MBDoE) framework that integrates physics-informed models, nonlinear regression, and information criteria to postulate, select and calibrate the best model to describe and optimize the AJP manufacturing process. Starting with already available data from system commissioning (e.g., prior single variable sensitivity analysis), four candidate physics-informed models are postulated and trained. MBDoE identifies a single additional optimal experiment to validate these predictive models with quantified uncertainties, which are then used to determine the best experimental conditions to control printed film thickness. As a comparative benchmark, the analysis is repeated using the same dataset with nonparametric Gaussian process regression (GPR) model that does not incorporate physical information. Using MBDoE principles, we find that only five experiments are necessary to calibrate the nonlinear physics-informed parametric model, and with said limited data, this model outperforms the black-box machine learning GPR model. This key result underscores an emerging trend in the data science community: incorporating physical information into predictive models often drastically reduces the data requirements. Leveraging MBDoE further increased the data efficiency. By design, the proposed data science framework is general in nature and can be easily extended to other experimental and additive manufacturing systems beyond AJP.

Aerosol jet printing↗
DOE OSTI2023

Developing a 20-year high-resolution wind data set for Puerto Rico

The purpose of this study is to develop a high-resolution wind resource data set for Puerto Rico as part of the wind resource assessment in the Puerto Rico Grid Resilience and Transition to 100 % Renewable Energy Study (PR100) project. The Weather and Research and Forecasting (WRF) is used to model 20-years (2001-2020) of wind resource data on a 3-km grid for the Puerto Rico region. Because accurately representing the planetary boundary layer (PBL)-physics in the WRF is key to accurately model low-level wind speed, 11 different PBL schemes are examined and evaluated to find a WRF configuration that can provide the most accurate wind data. The modeled wind speeds are validated with buoy observations, and the Shin-Hong PBL scheme is selected to generate the final wind data set. Here, the overall results demonstrate that the high-resolution data correctly represents the climate of Puerto Rico (e.g., a dominant easterly trade wind). At 160 m above ground, the southern regions of Puerto Rico show strong offshore wind speed (>8 m/s on average) throughout the daytime and nighttime. For land-based wind, average wind speed ranges from 5 m/s-7 m/s during daytime, whereas notable high wind speeds (>9 m/s) appear in the mountain regions during nighttime.

17 WIND ENERGY↗
DOE OSTI2024

Stochastic reconstruction of fracture network pattern using spatial point processes

Fracture spatial patterns can strongly affect fluid flow in the subsurface. Proximity and distribution of fractures control reservoir flow behavior over various length scales. In many studies, however, simplified geometrical patterns are generated for fractures which may lead to unrealistic subsurface models. Here we introduce a new method for characterization and modeling of fracture spatial patterns based on outcrop observations. We use Ripley's K-function to characterize the arrangement of fracture barycenters and intersection points over various length scales. In addition, we use semivariograms to quantify spatial correlation in fracture intensity maps. Using this information, we develop a stochastic algorithm that generates two-dimensional fracture network realizations with spatial properties similar to those of a real fracture network measured in the field. Numerical simulation models indicate that the generated fracture realizations exhibit similar flow behaviors as that of the original fracture network. Furthermore, such modeling tools expand and improve our capability in building representative fracture models and in quantification of uncertainty in naturally and hydraulically fractured reservoirs.

58 GEOSCIENCES↗
DOE OSTI2022

Dynamic risk assessment for geologic CO 2 sequestration

At a geologic CO 2 sequestration (GCS) site, geologic uncertainty usually leads to large uncertainty in the predictions of properties that influence metrics for leakage risk assessment, such as CO 2 saturations and pressures in potentially leaky wellbores, CO 2 /brine leakage rates, and leakage consequences such as changes in drinking water quality in groundwater aquifers. The large uncertainty in these risk-related system properties and risk metrics can lead to over-conservative risk management decisions to ensure safe operations of GCS sites. The objective of this work is to develop a novel approach based on dynamic risk assessment to effectively reduce the uncertainty in the predicted risk-related system properties and risk metrics. We demonstrate our framework for dynamic risk assessment on two case studies: a 3D synthetic example and a synthetic field example based on the Rock Springs Uplift (RSU) storage site in Wyoming, USA. Results show that the U.S. National Risk Assessment Partnership’s Open Source Integrated Assessment Model (NRAP-Open-IAM) coupled with a conformance evaluation can be used to effectively quantify and reduce the uncertainty in the predictions of risk-related system properties and risk metrics in GCS.

58 GEOSCIENCES↗
DOE OSTI2023

A hybrid data-driven and model-based approach for computationally efficient stochastic unit commitment and economic dispatch under wind and solar uncertainty

Stochastic unit commitment (UC) and economic dispatch (ED) are imperative in dealing with uncertainty in renewable forecast for power system operation and planning such that the overall expected production cost is minimized over the planning horizon. However, accurate calculation of the expected production cost requires assessment of a very large number of different scenarios of uncertain renewable resources, such as solar and wind, which is practically infeasible to simulate in real time. This article proposes a hybrid datadriven and physics-based model-predictive paradigm to efficiently solve for stochastic unit commitment and economic dispatch considering uncertainty in wind and solar power forecasts. Here, the novelty of the approach lies in decoupling the production cost estimation from the unit commitment and economic dispatch optimization problems under uncertainty without compromising on the fidelity of the solutions. A data-driven machine learning model is first developed to predict the mean optimal production cost. A physics-based inverse problem is then solved to get the stochastic UC and ED profiles from the expected cost. The presented approach considers, for the first time, solar uncertainty in UC/ED determination and enables efficient and accurate propagation of wind and solar uncertainty to estimate the statistics of the production cost. The effectiveness of the developed approach is demonstrated systematically on a stylized RTS-GMLC single-node system. The overall framework predicts the expected cost 62.5% more accurately than the existing state-of-the-art, on unforeseen days during the entire year, and yields, for the first time, the associated physically consistent UC and ED profiles. The solutions are also shown to be flexible in providing adequate daily reserves to address any statistical deviations from probabilistic power forecasts. The computational time associated with the presented method is only about 10 s compared to over 24 h needed for a conventional stochastic UC/ED determination under uncertainty on an Intel Core i9 processor with 32 GB of RAM.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2023

Isotherm modeling and techno-economic analysis of a TSA moving bed process using a tetraamine-appended MOF for NGCC applications

Tetraamine-appended metal-organic frameworks (MOF) are a new family of amine-functionalized MOF materials that show potential for CO 2 capture from flue gas conditions relevant to natural gas combined cycle (NGCC) power plants. This work presents isotherm modeling of the tetraamine-appended MOF Mg 2 (dobpdc)(3-4-3)(dobpdc 4- =4,4'-dioxidobiphenyl-3,3'dicarboxylate;3-4-3=N,N'bis(3-aminopropyl)-1,4-diaminobutane), process modeling, scale up, and a techno-economic optimization of a moving bed Temperature Swing Adsorption (TSA) process for carbon capture using this sorbent. This MOF exhibits a unique two-step CO 2 adsorption profile in three different pressure ranges. Thus, arctangent-based logistic functions and, quadratic and Langmuir models were employed to represent such isotherm behavior. The results of the isotherm model show good fitting vs the experimental data with an RMSE of 0.41. Here, to model the carbon capture process, the isotherm model was embedded into a moving bed contactor model, and this was used to simulate a TSA CO 2 capture cycle and evaluate cost-optimal designs considering flue gas from a -650 MWe NGCC power plant. The capital cost model consists of CAPEX correlations for reactors, compressors, ducting, etc., while the operating costs include steam, water, chemicals, and electricity (following NETL's quality guidelines for energy systems studies). A techno-economic optimization of the capture system was performed by using NETL's Framework for the Optimization and Quantification of Uncertainty and Surrogates tool (FOQUS). Results suggest that a moving bed carbon capture system with tetraamine-appended MOF can be competitive compared to conventional MEA solvent-based capture processes for NGCC plants, when a heat recovery efficiency of at least 40% is achieved, and MOF materials can be produced at a cost below -$9/kg.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Experimental measurements of fluid flow in an 84-pin hexagonal rod bundle with spacer grid for a gas-cooled fast modular reactor

A 50 MW e helium-cooled fast modular reactor (FMR) is under development, and as part of the Department of Energy Integrated Research Project (IRP), Texas A&M University is conducting the thermal-hydraulic characterization of its baseline core configuration. Here, we experimentally investigated the axial and cross flow fields characteristics in the hexagonal fuel rod bundle composed of 84 rods, a central rod, and spacer grids at a Reynolds number of 12,000. A fully transparent experimental facility resembling of one unit of the fuel assembly was constructed. Time-resolved particle image velocimetry (TR-PIV) measurements were performed to characterize hydraulic behavior downstream the spacer grid. Velocity measurements were conducted in the axial and radial direction of the rod bundle. From the PIV velocity vector fields, the full-field flow statistics were computed for the mean velocity, vorticity, and Reynolds stresses. An analysis of the energy decay downstream of the spacer grid was conducted with calculations of secondary-flow intensities, turbulent kinetic energy, power spectrum, and spatial-temporal velocity cross correlations. The vorticity field was obtained and pairs of counter-rotating vortexes were identified using a 3D reconstruction of several measurement planes. The data from this experimental campaign will be used to validate numerical models based on Computational Fluid Dynamics and other codes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

A predictive discrete-continuum multiscale model of plasticity with quantified uncertainty

Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of uncertainty in the computational predictions delivered by them. In this work, a sequential multiscale model has been developed, incorporating discrete dislocation dynamics (DDD) simulations and a strain gradient plasticity (SGP) model to predict the size effect in plastic deformations of metallic micro-pillars. The DDD simulations include uniaxial compression of micro-pillars with different sizes and over a wide range of initial dislocation densities and spatial distributions of dislocations. An SGP model is employed at the continuum level that accounts for the size-dependency of flow stress and hardening rate. Sequences of uncertainty analyses have been performed to assess the predictive capability of the multiscale model. The variance-based global sensitivity analysis determines the effect of parameter uncertainty on the SGP model prediction. The multiscale model is then constructed by calibrating the continuum model using the data furnished by the DDD simulations. A Bayesian calibration method is implemented to quantify the uncertainty due to microstructural randomness in discrete dislocation simulations (density and spatial distribution of dislocations) on the macroscopic continuum model prediction (size effect in plastic deformation). Here, the outcomes of this study indicate that the discrete-continuum multiscale model can accurately simulate the plastic deformation of micro-pillars, despite the significant uncertainty in the DDD results. Additionally, depending on the macroscopic features represented by the DDD simulations, the SGP model can reliably predict the size effect in plasticity responses of the micropillars with below 10% of error.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Mesoscale informed parameter estimation through machine learning: A case-study in fracture modeling

Scale bridging is a critical need in computational sciences, where the modeling community has developed accurate physics models from first principles, of processes at lower length and time scales that influence the behavior at the higher scales of interest. However, it is not computationally feasible to incorporate all of the lower length scale physics directly into upscaled models. This is an area where machine learning has shown promise in building emulators of the lower length scale models, which incur a mere fraction of the computational cost of the original higher fidelity models. We demonstrate the use of machine learning using an example in materials science estimating continuum scale parameters by emulating, with uncertainties, complicated mesoscale physics. Additionally, we describe a new framework to emulate the fine scale physics, especially in the presence of microstructures, using machine learning, and showcase its usefulness by providing an example from modeling fracture propagation. Our approach can be thought of as a data-driven dimension reduction technique that yields probabilistic emulators. Our results show well-calibrated predictions for the quantities of interests in a low-strain simulation of fracture propagation at the mesoscale level. Furthermore, on average, we achieve ~10% relative errors on time-varying quantities like total damage and maximum stresses. Successfully replicating mesoscale scale physics within the continuum models is a crucial step towards predictive capability in multi-scale problems.

36 MATERIALS SCIENCE↗